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Published online by Cambridge University Press: 02 November 2018
Chapter Istudies the category of commutative integral monoids, especiallyso-called “fine monoids”which are the basic building blocks of toric and logarithmic geometry.It includes a self-contained treatment of standard results in convex geometry, including finiteness and duality and the geometry of faces and ideals, and also discusses the affine toric varieties arising from monoid algebras.In addition to these classical results, it includes a study of limits and colimits of monoids, of actions of monoids on sets,and ofhomomorphisms of monoids, including the key concepts of exact, integral, and saturated homomorphisms.
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